For using the available band in an effective manner, digital transmission systems may make use of multilevel modulation techniques. The system threshold with respect to thermal noise increases with increasing spectral efficiency and, in order to obtain a desired Bit Error Rate (hereinafter BER), greater values of the transmitted power are necessary. Such power is limited by the input-output characteristic of the transmitter final amplifier which is here structured as a nonlinear channel without storage.
When solid state amplifiers are used and/or when predistortion techniques without storage are utilized (see, e.g., G. Karam and H. Sari, "Analysis of predistortion, equalization and ISI cancellation techniques in digital radio systems with nonlinear transmit amplifiers", IEEE Transactions on Communications, vol. 37, No. 12, Dec. 1989), the input-output characteristic of the nonlinear channel (comprising in it also the effect of the amplifiers and of eventual predistortions) in practice is that of a hard limiter.
If a distortion-free transmission is desired, the peak of the complex envelope of the signal at the input of the nonlinear channel defined above must not go beyond the saturation point. The basic technique (see, e.g., T. Ryu, J. Uchibori and Y. Yoshida, "A stepped-square 256-QAM for digital radio systems", ICC '86, vol. 3, pages 1477-1481, June 1986) being used in order to avoid great values of the peak power, is to design the two-dimension constellation (hereinafter 2D) in such a way that the peak power of the unfiltered signal is as small as possible still observing the two restrictions of the assigned rate and of the minimum distance between the points of the transmitted constellation.
An alternative approach (still observing the two restrictions mentioned above) is disclosed in the European Patent Application EP93111722, filed by the applicant, titled "Method and Apparatus for reducing the peak power of data sequences", inventors A. Sandri and A. Spalvieri, where it is emphasized that, to improve the efficiency of a digital link (e.g., a microwave one), it is useful to focus on the peak power of the filtered signal transmitted. The aforementioned European patent Application has a U.S. counterpart, i.e., U.S. Pat. No. 5,493,587, claiming priority from the same parent, i.e., Italian application MI 92A001819, filed Jul. 27, 1992.
In order to reduce such power, in the above mentioned patent application, A. Sandri and A. Spalvieri propose to use, in transmission, an encoder disposed between the modulator and the transmit filter, and, in reception, a decoder disposed between the receive adapted filter and the demodulator.